eprintid: 975
rev_number: 9
eprint_status: archive
userid: 36
dir: disk0/00/00/09/75
datestamp: 2011-10-31 11:23:14
lastmod: 2011-11-17 14:44:57
status_changed: 2011-11-17 14:44:57
type: article
metadata_visibility: show
creators_name: Berti, Patrizia
creators_name: Crimaldi, Irene
creators_name: Pratelli, Luca
creators_name: Rigo, Pietro
creators_id: 
creators_id: irene.crimaldi@imtlucca.it
creators_id: 
creators_id: 
title: A central limit theorem and its applications to multicolor randomly reinforced urns
ispublished: pub
subjects: HA
subjects: QA
divisions: EIC
full_text_status: none
keywords: Bayesian statistics; central limit theorem; empirical distribution; Poisson-Dirichlet process; predictive distribution; random probability measure; stable convergence; urn model
abstract: Let Xn be a sequence of integrable real random variables, adapted to a filtration (Gn). Define Cn = √{(1 / n)∑k=1nXk - E(Xn+1 | Gn)} and Dn = √n{E(Xn+1 | Gn) - Z}, where Z is the almost-sure limit of E(Xn+1 | Gn) (assumed to exist). Conditions for (Cn, Dn) → N(0, U) x N(0, V) stably are given, where U and V are certain random variables. In particular, under such conditions, we obtain √n{(1 / n)∑k=1nX_k - Z} = Cn + Dn → N(0, U + V) stably. This central limit theorem has natural applications to Bayesian statistics and urn problems. The latter are investigated, by paying special attention to multicolor randomly reinforced urns. 
date: 2011
date_type: published
publication: Journal of applied probability 
volume: 48
number: 2
publisher: Applied Probability Trust
pagerange: 527-546
id_number: 10.1239/jap/1308662642
refereed: TRUE
issn: 0021-9002
official_url: http://projecteuclid.org/euclid.jap/1308662642
citation:   Berti, Patrizia and Crimaldi, Irene and Pratelli, Luca and Rigo, Pietro  A central limit theorem and its applications to multicolor randomly reinforced urns.  Journal of applied probability , 48 (2).  pp. 527-546.  ISSN 0021-9002      (2011)